# Lowest Common Multiples

*Keywords:*

AO elaboration and other teaching resources

Identify highest common factors and least common multiples.

Number Framework Stage 8

#### Using Number Properties

Problem: “Two salesmen are in Timaru today. John returns to Timaru every 4 days, and Martin visits every 6 days. What days will they both be in Timaru?”

Draw the table on the board and discuss how to fill it in. The first few entries have been made.)

“What are the common factors of 4 and 6? What is the LCM of 4 and 6?” *(Answer: 12, 24, 36, ... LCM = 12.)*

Problem: “John visits Greymouth every 20 days, and Martin visits every 12 days. How often are they in Greymouth together?”

Examples: Find the LCMs of these pairs: 6 and 9, 12 and 18, 20 and 25, 25 and 10, 12 and 18, 5 and 6, 10 and 11

Problem: “Josie knows that finding the LCM of 51 and 136 will be tedious by listing common multiples. So she summarises the answers above and looks for a pattern. Josie spots a link between the LCM, the product of the numbers, and the HCF. What is it?

Explore whether the pattern always works.”

*(Answer: LCM = product *÷ *HCF in all cases.)*

Examples: Find the LCMs of these pairs of numbers: 49, 112 156, 65 738, 615, 910, 728 459, 1 917 ...

#### Understanding Number Properties:

The LCM of any two numbers a and b can be found by ...(*Answer: dividing a x b by the HCF of a and b.)*